We provide further intuition for our usage of within-group AUC and xAUC. Recall that the AUC is the probability that a randomly chosen positive example, \(x_i\) , has a greater risk score, than a randomly chosen negative example, \(x_j\)  (i.e., \(P(s(x_i)>s(x_j))\) ). The within-group AUC for group \(a\) , written as \(\text{AUC}_a\) , is thus the AUC considering only examples in group \(a\)  (Figure REF , cyan). The xAUC has a similar interpretation: \(\text{xAUC}_{a, a^{\prime }}\)  is the probability that a randomly chosen positive example from group \(a\)  is scored above a randomly chosen negative example from group \(a^{\prime }\)  (Figure REF , magenta). We defer to [1]} for details on xAUC.
